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Weak approximation of killed diffusion using Euler schemes

Emmanuel Gobet

Stochastic Processes and their Applications, 2000, vol. 87, issue 2, 167-197

Abstract: We study the weak approximation of a multidimensional diffusion (Xt)0[less-than-or-equals, slant]t[less-than-or-equals, slant]T killed as it leaves an open set D, when the diffusion is approximated by its continuous Euler scheme or by its discrete one , with discretization step T/N. If we set [tau] := inf{t>0: Xt[negated set membership]D} and , we prove that the discretization error can be expanded to the first order in N-1, provided support or regularity conditions on f. For the discrete scheme, if we set , the error is of order N-1/2, under analogous assumptions on f. This rate of convergence is actually exact and intrinsic to the problem of discrete killing time.

Keywords: Weak; approximation; Killed; diffusion; Euler; scheme; Error's; expansion; Malliavin; calculus; Ito's; formula; Orthogonal; projection; Local; time; on; the; boundary (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (43)

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